1. Field of Invention
The field of the currently claimed embodiments of this invention relates to systems and methods for registering images, and more particularly to systems and methods for registering images in an N dimensional space using N+M dimensions.
2. Discussion of Related Art
Ongoing advances in cone-beam computed tomography (CBCT) enable high-quality 3D imaging for image-guided interventions, including image-guided radiation therapy (IGRT) and image-guided surgery (IGS). The ability to acquire up-to-date images in the course of intervention offers the potential to overcome the limitations of conventional image guidance systems that operate in the context of preoperative data only and fail to account for anatomical change occurring during therapy. Such systems have entered broad application in IGRT,1 cardiovascular interventions,2 and high-precision IGS including orthopaedic/spine surgery3,4 and head and neck/skull base surgery.5-8 
Key to many of these applications is the ability to register preoperative images (e.g., preoperative CT along with registered MR or PET images) and planning data to intraoperative CBCT. Such registration algorithms must be sufficiently fast and well integrated so as not to impede surgical workflow and provide sufficient geometric accuracy for the particular interventional task. Rigid registration is often insufficient due to variation in patient positioning between preoperative and intraoperative setups as well as anatomical deformations occurring during intervention. In head and neck/skull base surgery (the focus of examples below), despite the largely rigid anatomical context, rigid registration alone fails to account for independent (piecewise-rigid) motion of the neck, jaw, and skull as well as soft-tissue deformations occurring during the procedure—e.g., displacement of sinus contents, herniation of the orbital wall/lamina papyracea, and deformation of the tongue and oropharynx.
These challenges motivated previous work in developing a variant of the Demons registration method9-13 well suited to CBCT-guided procedures.14 The method includes: i.) a basic morphological pyramid providing registration within ˜20 s; ii.) a “smart” convergence criterion that automatically advances each level of the pyramid to achieve sub-voxel (˜0.5 mm) registration accuracy and eliminate extraneous iterations;15 and iii.) an intensity matching step concurrent with the iterative registration process to provide robustness against image intensity (voxel value) mismatch in CT-to-CBCT or CBCT-to-CBCT registration.16 
In addition to the basic challenges of tissue deformation in image-guided procedures is a novel and largely unaddressed problem: what if the differences between the preoperative (“moving”) image and the intraoperative (“fixed”) image involve not only tissue deformation but also the physical removal of mass? In IGRT, an example of a missing tissue problem is weight loss over the course of multiple radiotherapy fractions. In IGS, the problem can be more explicit and includes the physical resection of tissues on surgical approach (e.g., excision of ethmoid air cells on approach to the sphenoid sinus) and removal of the surgical target itself (e.g., drillout of a bony lesion). The behavior of deformable registration algorithms in the presence of missing tissue is an important consideration, since straightforward application of conventional registration approaches may lead to spurious distortion in regions of mismatch—which are often the regions of primary interest (e.g., in proximity to a partially resected surgical target). Registration in the presence of large surgical excisions presents new technical challenges compared to registration in the presence of deformations alone. Similarly, registration in the presence of structures added to the fixed image (e.g., surgical devices) presents a significant challenge. Accordingly, there remains a need for improved systems and methods for registering images.